The Limit Assumption

Stefan Kaufmann

Abstract

In the literature on modality and conditionals, the Limit Assumption is routinely invoked to ensure that a simple definition of necessity (truth at all minimal worlds) can safely be substituted for a more complicated one (cf. Lewis’s and Kratzer’s definitions involving multiple layers of quantification). The Limit Assumption itself was formulated by David Lewis in 1973 and 1981, and while its plausibility has at times been debated on philosophical grounds, its content is rarely questioned. I show that there is in fact no single “correct” Limit Assumption: which one is right depends on structural properties of the model and the intended notion of necessity. The version that is most widely appealed to in the linguistic literature turns out to be incorrect for its intended purpose. The source of the confusion can be traced back to Lewis himself.